Surface acoustic-wave attenuation by a two-dimensional electron gas in a strong magnetic field.

The propagation of a surface acoustic wave (SAW) on GaAs/AlGaAs heterostructures is studied in the case where the two-dimensional electron gas (2DEG) is subject to a high magnetic field and a smooth random potential with correlation length Λ and amplitude ∆. The electron wave functions are described in a quasiclassical picture using results of percolation theory for two-dimensional systems. We focus on the situation where the electron drift velocity vD is smaller than the sound velocity vs, restricting the absorption of surface phonons at a filling factor ν̄ ≈ 1/2 to electrons occupying extended trajectories of fractal structure. Both piezoelectric and deformation potential interactions of surface acoustic phonons with electrons are considered and the corresponding interaction vertices are derived. These vertices are found to differ from those valid for three-dimensional bulk phonon systems with respect to the phonon wave vector dependence. We derive the appropriate dielectric function ε(ω, q) to describe the effect of electron-electron interactions on